All digital communication receivers are faced with the task of estimating the transmitted signal with the greatest degree of accuracy, while performing the operation as rapidly and simply as possible. In practice, there is an inevitable trade-off between decoding accuracy and speed of processing.
It is possible to exhaustively search all of the possible signal combinations that, when modified by the channel, could have resulted in the received signal. Unfortunately, this process, of considering every conceivable signal combination that could have generated a specific signal is extremely complex. The problem is compounded for high data rate systems that employ multiple element transmit and receive antennas.
A particular problem arises in a communications links where a transmitter with more than one transmit antenna is employed since signals received from different transmit antennas interfere with one another. This results in so-called multi-stream interference (MSI) and causes decoding difficulties. The potential advantage, however, is greatly increased throughput (that is, a higher bit rate) for such a communications link. In this type of MIMO (Multiple-input Multiple-output) communication link the “input” (to a matrix channel) is provided by the transmitter's plurality of transmit antennas and the “output” (from a matrix channel) is provided by a plurality of receive antennas. Thus each receive antenna receives a linear combination of signals from all the transmitter's transmit antennas and the separate signals sent from each transmit antenna must be extracted from this combination.
A typical wireless network comprises a plurality of mobile terminals (MT) each in radio communication with an access point (AP) or base station of the network. The access points are also in communication with a central controller (CC) which in turn may have a link to other networks, for example a fixed Ethernet-type network. Until recently considerable effort was put into designing systems so as to mitigate for the perceived detrimental effects of multipath propagation, especially prevalent in wireless LAN (local area network) and other mobile communications environments. However it has been recognised that multipath propagation can be used to an advantage, as in effect, this uniquely affects or labels a spatial path, facilitating the separation of the superposition of signals at the receiver. Work G. J. Foschini and M. J. Gans, “On limits of wireless communications in a fading environment when using multiple antennas” Wireless Personal Communications vol. 6, no.3, pp. 311-335, 1998 has shown that by utilising multiple antenna architectures at both the transmitter and receiver (a so-called multiple-input multiple-output (MIMO) architecture) increased channel capacities are possible (in effect, spatial multiplexing). Attention has also turned to the adoption of space-time coding techniques (in OFDM, space-frequency coding) for wideband channels. Typically channel state information (CSI) for maximum likelihood detection of such coding is acquired via training sequences and the resulting CSI estimates are then fed to a Viterbi decoder.
Another technique for space-time code detection in a MIMO system based upon the use of periodic pilot sequences and interpolation filters is described in A. Naguib, V. Tarokh, N Seshadri and A. Calderbank “A space-time coding based model for high data rate wireless communications” IEEE J-SAC vol. 16, pp. 1459-1478. Octocber 1998. However this is a diversity technique which does not directly increase the bit rate.
FIG. 1 shows a simple example of MIMO communication system 100 in which an information source 102 provides information symbols s(t) at time t which are transmitted simultaneously, that is, spatially multiplexed, from transmit antennas 104. These symbols can be interrelated through coding. A plurality M of receive antennas 106 receives respectively signals r1(t), . . . rm(t) which are input to receiver 108. The receiver 108 provides on output 110 an estimate ŝ(t) of the transmitted symbol ŝ (t). There is a plurality of channels between the transmit and receive antennas, for example all channels with two transmit antennas and two receive antennas. Periodic pilot sequences in the transmitted signal may be used to estimate the time varying responses of these channels.
Third generation mobile phone networks use CDMA (Code Division Multiple Access) spread spectrum signals for communicating across the radio interface between a mobile station and a base station. These 3G networks are encompassed by the International Mobile Telecommunications IMT-2000 standard (www.ituint) and the UMTS (Universal Mobile Telecommunications System) system is the subject of standards produced by the Third Generation Partnership Project (3GPP, 3GPP2), technical specifications for which can be found at www.3gpp.org. Fourth generation mobile phone networks and other communications systems, although not yet defined, may employ MIMO-based techniques.
In practical data communication systems multipath propagation within a channel results in intersymbol interference (ISI), which is often corrected with a combination of equalisation and forward error correction (FEC) coding. For example a linear equaliser effectively deconvolves the received data from the channel impulse to produce data estimates with ISI substantially removed. Alternatively OFDM may be employed to effectively define a series of narrowband channels and avoid ISI by the use of a guard interval and cyclic prefix. An optimal equaliser may employ maximum likelihood (ML) sequence estimation or maximum a priori estimation (MAP), for example using a Viterbi algorithm. Where data has been protected with a convolutional code a soft input Viterbi decoder may be employed, usually together with data interleaving to reduce the effects of burst errors. Such approaches provide optimal equalisation but become impractical as the symbol alphabet size and sequence length (or equivalently channel impulse response length) increases.
Turbo equalisation achieves results which are close to optimal but with substantially reduced complexity compared to non-iterative joint channel equalisation and decoding. Broadly speaking turbo equalisation refers to an iterative process in which soft (likelihood) information is exchanged between an equaliser and a decoder until a consensus is reached. The effect of the channel response on the data symbols is treated similarly to an error correction code and typically a soft output Viterbi algorithm (SOVA) is used for both. Again, however, such techniques are impractically complex for large delay spreads and symbol alphabets, particularly as several processing iterations may be needed to achieve convergence for a single data block. These difficulties are significantly exacerbated where signals from more than one transmit antenna must be disentangled and equalised, with a different channel response for each transmit antenna or transmit-receive antenna pair.
The exhaustive search described above, grows exponentially in complexity with the number of channel taps, the size of the constellation and the number of MIMO sub-channels. For practical MIMO systems this optimum solution imposes far too heavy a burden on the processor of the receiver.
An alternative detection method to exhaustive searching is to use computationally simpler linear filtering, which performs decoding based on minimisation of some error metric, such as minimum mean square error (MMSE). Unfortunately, these methods have relatively poor performance for MIMO systems.
Outside the context of telecommunications systems, where different problems are encountered, a particle filtering-based statistical technique has been used for speech processing (see W. Fong, S. J. Godsill, A. Doucet, and M. West, “Monte Carlo smoothing with applications to audio signal enhancements”, IEEE Trans Signal Proc, vol 50, no 2 pp 438-488, 2002).
There is therefore a need for reduced computational complexity equalisation and decoding methods and apparatus, for example, for applications in MIMO systems.